On-line monitoring of the characteristics of an electrical umbilical cable, such as an underwater (for example subsea) well control system umbilical cable, is performed by an umbilical monitoring device (UMD) which applies an electrical signal to conductors of the umbilical cable with respect to earth and uses various measuring techniques to ascertain that the characteristics of the umbilical cable are adequate for its intended remaining lifetime. The measuring techniques in such a UMD employ electronic amplifiers which are protected from excessive voltages on the live system by a fast blow fuse in series with the live system. The problem is that, if the fuse has blown, the UMD believes that it is connected to an umbilical cable with a high electrical insulation resistance, even if the insulation has completely failed.